“Recursive” is a reasonable term because the generation N AIs will train the Generation N+1 AIs. The term “iterative” doesn’t reflect this nuance as well IMO.
Recursion reduces each step toward a base case: each step is defined in terms of previous/simpler steps, not more advanced ones. The "recursive" in "recursive self improvement" has things precisely backward. Iteration correctly describes a process where each step is the starting point of its successive step, so it should be "iterative self improvement" but I guess that didn't sound as cool.
I think you're confusing a recurrence relationship with recursive execution. Until AI has control over its inputs (including physical inputs - compute hardware, etc.) it's not quite RSI. We'll get there. They'll get there, rather.
